Orthogonal frequency division multiplexing (OFDM) is one of the technologies considered for 4G broadband wireless communications due to its robustness against multipath fading and relatively simple implementation compared to single carrier systems. To preserve both amplitude and phase information, OFDM transmitters utilize linear power amplifiers. One of the main drawbacks of using OFDM is the high cost of linear power amplifiers with high dynamic range. Such amplifiers are used because the OFDM signals have a high peak-to-average power ratio (PAPR), particularly since the OFDM signal will usually consists of a large number of subcarriers.
Various techniques have been proposed to reduce the PAPR of OFDM signals. For example the following publications describe some of these techniques: J. Davis and J. Jedwab, “Peak-to-mean power control in OFDM, Golay Complementary Sequences, and Reed-Muller Codes,” IEEE Transactions on Information Theory, Vol. 45, pp. 2397–2417 (November 1999); A. D. S. Jayalath and C. Tellambura, “Reducing the Peak-to-Average Power Ratio of an OFDM Signal Through Bit or Symbol Interleaving,” IEEE Electronics Letters, Vol. 36, pp. 1161–1163 (June 2000); and H. Ochiai and H. Imai, “Performance Analysis of Deliberately Clipped OFDM Signals,” IEEE Transactions on Communications, Vol. 50, pp. 89–101 (January 2002), the entire disclosures of each of these publications are incorporated herein by reference.
With respect to the latter approach, the deliberate clipping of the OFDM signal before amplification is a simple and efficient way of controlling the PAPR. The clipping process is characterized by the clipping ratio (CR), defined as the ratio between the clipping threshold and the RMS level of the OFDM signal. Clipping is a non-linear process, which may lead to significant distortion and performance loss. In particular, clipping at the Nyquist sampling rate will cause all the clipping noise to fall in-band and suffers considerable peak re-growth after digital to analog (D/A) conversion.
In the H. Ochiai and H. Imai paper and in X. Li and L. J. Cimini, “Effects of Clipping and Filtering on the Performance of OFDM,” in Proc. IEEE Vehicular Technology Conf. (VTC), pp. 1634–1638 (May 1997) (the entire disclosure of which is hereby incorporated by reference), it was shown that clipping an over-sampled OFDM signal reduces the peak re-growth after D/A conversion and generates less in-band distortion. But this technique causes out-of-band noise that needs to be filtered.
The problem of distortion caused by intentional clipping and the attendant out-of-band noise is a significant issue in connection with using OFDM, particularly since clipping noise is the significant factor limiting performance in OFDM systems operating at high signal to noise ratio (SNR).
Although techniques have been proposed for mitigating the effect of clipping noise, they are less than satisfactory. The following publication illustrate this point: D. Kim and G. L. Stuber, “Clipping Noise Mitigation for OFDM by Decision-aided Reconstruction,” IEEE Communications Letters, Vol. 3, pp. 4–6 (January 1999); and H. Saedi, M. Sharif, and F. Marvasti, “Clipping Noise Cancellation in OFDM Systems Using Oversampled Signal Reconstruction,” IEEE Communications Letters, Vol. 6, pp. 73–75 (February 2002). In both cases, however, acceptable loss in SNR (e.g., about less than 1 dB) is achieved only for CR≧4 dB. Furthermore, the decision aided reconstruction approach described in the D. Kim and G. L. Stuber publication only applies to Nyquist rate clipping. Finally, the use of over-sampled signal reconstruction disclosed in the H. Saedi, M. Sharif, and F. Marvasti publication also requires significant bandwidth expansion to work well.
A fundamental characteristic of these approaches, as well as other proposed methods, is that they attempt to reconstruct the affected (or lost) time domain signal samples resulting from clipping. It is believed that the reconstruction of time domain signals is inherently error prone and, thus, undesirable.
Accordingly, there are needs in the art for new methods and apparatus for processing OFDM signals in order to at least one of reduce PAPR, reduce distortion and out of band radiation.